Online scheduling with hard deadlines on parallel machines

Abstract

In this paper, motivated by on-line admission control in the hard deadline model, we deal with the following scheduling problem. We are given m identical machines (multi-streams). All jobs (requests) have identical processing time. Each job is associated with a release time and a deadline, neither of which is known until the job arrives. As soon as a job is available, we must immediately decide if the job is accepted or rejected. If a job is accepted, then it must be completed no later than its deadline. The goal is to maximize the total number of jobs accepted. The one-machine case has been extensively studied while little is known for multiple machines. Our main result is deriving a nontrivial optimal online algorithm with competitive ratio 3/2 for the two-machine case by carefully investigating various strategies. Deterministic lower bounds for the general case are also given. © Springer-Verlag Berlin Heidelberg 2006.